Exampleet( ) be the solution with( ) i eykyutut+=&111Let () be the solution with (), i.e. d( ) be the solution with( ) i eytyutut&222and () be the solution with (), i.e. hen for any input ( )( )( ) we can verifyatyutu t+&2 2Then for any input ()()() we can verify thatαα=+( )( )( )y tsatisfies the equation: -- ()-()yuyykyyuu+++&&&112222=(-)(-)0ykyuykα+++=

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Signal DecompositionSuperposition shows that if we can decompose a general signal into a set of elementary signals, then the response an be obtained by appropriately summing thecan be obtained by appropriately summing the responses to all the elementary signals. ()ip tctceδ+Typical Elementary Signals: impulse and exponentialii∑Hint: any signal represented by a Laplace Transform U(s), it can be expanded as and the inverse Laplace Transform is iiiccsp+−∑ip tiice+∑

ImpulseThe impulse is represented by()tδThe impulse can be regarded as a signal with huge magnitude in an extremely short duration.

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